In a vehicle including a power connecting/disconnecting device interrupting power transmission between an engine and drive wheels, a vehicle running control device is conventionally known that interrupts the power transmission by the power connecting/disconnecting device during inertia running. For example, this corresponds to a clutch control device described in Patent Document 1. In Patent Document 1, a clutch disposed in a power transmission path acts as the power connecting/disconnecting device and, if an accelerator pedal is suddenly returned from a depressed state of the accelerator pedal, the clutch control device releases the clutch to interrupt the power transmission between the engine and the drive wheels. As a result, a fuel consumption rate can be improved.